Why do mathematicians allow themselves to magically invent things like complex numbers to get around finding the square root of a negative number which is supposed to be impossible, but when you try to invent a new number to get around division by zero they get all cunty?

>>11692660Because division by zero is absolutely, completely impossible. Complex numbers really aren't that far-fetched, just a way to represent something we otherwise cannot represent with our 1-dimensional mathematics.

>>11692660You CAN define division by zero and construct an algebraic structure with it if you want. No one is stopping you. I'm pretty sure "wheel thoery" is the study of "algebraic wheel", which are like rings but division by zero is possible and well defined. The Real numbers and any commutative ring can be extended to a wheel. Look into that if you like.

>>11692873>>11692660if you try to assign a single value to the division by 0, or try to treat division by 0 (or the multiplicative inverse of 0) as you would division by any other number (or as the multiplicative inverse of any other number) then you end up with contradictions and you will be able to "prove" things like 1 = 0. You don't end up with contradictions with imaginary numbers, however.

>>11692660Squaring negatives making a positive might sound intuitive, but it's just as arbitrary as i^2 equalling negatives. Makes sense they needed to invent i to fulling describe situations were the product of negative values doesn't make a positive etc.

>>11692863Division is (by definition) multiplication by the (multiplicative) inverse, i.e., a/b = a * (b)^(-1). Zero does not have a multiplicative inverse. Why? Suppose it did: let a be a real number such that 0*a = 1. But 0*a = (1-1)*a = a - a = 0 for any real number a, so 0 = 1, which contradicts a basic assumption about real numbers.

The one idea is very strange at first, but when played with a bit, turns out not to imply contradictions. If division by zero is allowed, this leads to contradictions. This is the difference between the two notions.

>>116947821/0 * 0/2 = 0 * 2 = 20 * 0 = 0If I have 0 nigger faggots and multiply them by 0 I'm not losing or gaining any more or fewer nigger faggots.Math supposed to be about counting real shit. The moment you detach it from reality with fag shit like infinity is when you create all kinds of paradoxes. Stay within limitations of reality and shit won't break. Otherwise it's just mental masturbation like how many devils you can fit on a needle head.

>>11695694Infinity isn't as toxic a construct as you have been lead to believe. When I calculate elements of a scattering matrix, I am actually calculating asymptotic values. A healthy concept of infinity is useful for this purpose.

It is not about mathematicians have goals when creating new math constructs.

99% time, it is more in the lines "I wonder what kind of crazy shit is going to happen if I assumed X to be true".It is usually much later when someone finds some actual use for made up shit like this.

2=1 isnt a contradiction when you realize division by zero returns the set of real numbers (a line) and the '=' sign doesn't mean what you think it means. That sign actually means to check for membership across sets on either side of the equation. Most of you are simply just used to the idea of doing equations with singleton sets so you think of true boolean equality when using the '=' sign in formulae.

>be John Maths>Proceed to invent mathematics>Forget to define division by 0>People who come after think you deliberately left it but just forget>Millennia of civilizations hampered by the lack of division by 0

>>11692660Why do mathematicians allow themselves to magically invent things like NEGATIVE numbers to get around finding solutions to equations like x+1=0?>"The basket contains -8 apples"lol like what do you even mean bro?

>>11692660Computer science as been operating for almost 40 years now with the notion of negative and positive zero in their numeric calculations.Negative zero.Are you kidding me.If shit like this has gone unchanged for 30 years despise absurdity of situation what makes you think almost dogmatic approach to mathematics will change anything.

>>11696502>Computer science as been operating for almost 40 years now with the notion of negative and positive zero in their numeric calculations.That is because floating points are fucking weird on PCs. Having negative and positive zeroes is just making things simpler.

>>11696516>negative and positive zeroes is just making things simpler.Insisting that this is the right way is precisely what im talking about.There are better ways of doing this and you are retarded just like the rest.Its not like you cant but you wont even try to escape the stupidity.

>no you cant just have a number system that will follow mathematical rules which were stone a millennia ago

>>11696547You sound like a pretty savvy guy.Maybe you could read my post,follow the link i provided for you and take it away from there with a google search.That should provide you with enough material to research this topic a bit.

>>11692660>magically invent things like complex numbersToo bad there's no magical invention. There's actually a robust proof for the complex plane that goes back centuries. Spivak starts the process at the end of his calculus book and leaves the rest of the exercise to the reader. It's pretty easy to follow once you've done the rest of the book before it. There's also real world application of complex numbers in places like electrical engineering if you just can't trust the math.>new number to get around division by zeroIf you believe you've done this, submit your proof for academic and peer review. Just realize that science and mathematics, by intention, are resistant to change without robust proof, so you may need to do more than shotgun it into a Laotian swamp-water gargling forum once to have your work recognized by the broader community.

>>11692660What are you talking about. Both complex numbers and extended real numbers have a theory. Look up things like meromorphic functions and one point compactifications. The theory of automorphisms on the complex field is wrapped up nicely when you use extended complex numbers. The issue is the common person is a complete idiot when they try to talk about things they dont understand. This is true for ANY field, not just math.

>>11692660Because dividing by zero makes you arrive at contradictions and it doesn’t make sense practically: you cannot divide any number of objects between zero people because there are no people to divide to, it can’t be zero because that implies someone to give zero things to which we don’t have.

Also as a contradiction 0/n = 0/1 = 0 ==> 1*0=n*0=0 ==> if k/0 = 1 that 1=n=0 and we know that one cannot be zero

All attempts to make numerical sense of division by zero (and likewise multiplication by zero) require that .You can say it's equivalent, or that the real part is 0. But to say it just equals zero is completely ignoring the premise.

I encourage all RIGHTEOUS defenders of the ONE TRUE FAITH to join with me in a HOLY CRUSADE against complex numbers, negative numbers, zero, reals, infinities and infinitesimals. And to retake Constantinople if we have time.

IN THE NAME OF GOD we shall put the practitioners of those abominations to the SWORD! Say it with me, Brothers and Sisters of the finite and discrete Universe. DEUS VULT! DEUS VULT! DEUS VULT!

>>11692863If you have 10 dollars and want to divide them equally among yourself and your four friends, how much does every person get?everyone gets 2 ( )

If you have 10 dollars and want to divide them equally among just yourself and none of your friends, how much does every person get?everyone gets 10 ( )

If you have 10 dollars and want to divide them equally among nobody, not even yourself, how much does every person get?the question becomes nonsense, the 10 bucks cant just disappear from existence ( )